Our main result Theorem REF  limits the potential advantage of quantum ML over classical ML for predicting outcomes of quantum experiments with a specified average-case prediction error. Our figure of merit is the number of times the quantum process \(\operatorname{{\mathcal {E}}}\)  must be accessed in the quantum and classical settings, disregarding other measures of runtime of the model. This information-theoretic analysis complements recent studies of the computational complexity of classical ML models trained with data from quantum experiments [1]}.
Together, these rigorous results indicate that classical ML trained using quantum measurement data can be surprisingly powerful, boosting our hopes that near-term experimental platforms [2]}, assisted by classical ML, may fruitfully address challenging quantum problems in physics, chemistry, and materials science.
